Morphology can be an important property in particle-related applications. The experimental determination of the fractal properties of nano-aggregates has been of interest for scientists and engineers as it can influence the physical and chemical properties of the aggregates. For example, morphology may be a factor in aerosol synthesis, which can be used for bulk production of nanomaterials, such as in—1) pharmaceuticals synthesis and processing, where the ability to control the size and state of aggregates can influence their behavior in the human body; 2) synthesis of printer toners, tires, paints, fillers, and fiber-optics products, where nanopowders morphology uniformity can influence product quality; and 3) carbon nanotube manufacturing, where uniformly sized and shaped carbon nanotubes may have desirable properties.
When used to produce particles beyond a certain length, aerosol formation mechanisms can produce aggregates. Aggregates can have complex, fractal-like morphologies, and particles having the same mass, such as being composed of the same number of individual particles, can have different morphologies, such as being more spherically or more linearly shaped.
Fractal mathematics have been used to quantify the morphology of solid nano-aggregates. For example, the Hausdorff or mass fractal dimension D can be used to characterize the complex shapes of nano-aggregates with:N=k0(Rg/dp)D where N is the number of monomers in an aggregate, D is the non-integer mass fractal dimension, k0 is the fractal prefactor, dp is the monomer diameter, and Rg is the radius of gyration of an aggregate.
Aggregates' fractal properties are often determined through quantitative analysis of digitized ex situ transmission/scanning electron microscopy (TEM/SEM) images and/or in situ light scattering measurements. Analysis of electron micrographs typically involves extraction of three-dimensional (3-d) structural and geometrical properties of aggregates, which are commonly unknown, from their two-dimensional (2-d) projected images.
It can be time consuming and difficult to accurately determine the morphology of aggregates. Commonly, to completely determine the shape of an aggregate, multiple two-dimensional images are obtained of an aggregate and composited to produce a three-dimensional representation of the object. Although some studies discuss simulation of aggregates, they can suffer from drawbacks. For example, one study discusses the simulation of aggregate formation under various regimes. The computational resources for such simulations can be rather high. Further, although the simulations purport to simulate the particles as they exist in a fluid, such as air, they do not appear to describe how the particles might appear when located on the surface, such as the surface of a filter or other collection device. Thus, the results of such simulations may not correlate with experimental data.